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We consider offline detection of a single changepoint in binary and counttime-series. We compare exact tests based on the cumulative sum (CUSUM) and thelikelihood ratio (LR) statistics, and a new proposal that combines exacttwo-sample conditional tests with multiplicity correction, against standardasymptotic tests based on the Brownian bridge approximation to the CUSUMstatistic. We see empirically that the exact tests are much more powerful insituations where normal approximations driving asymptotic tests are nottrustworthy: (i) small sample settings; (ii) sparse parametric settings; (iii)time-series with changepoint near the boundary.  We also consider a multichannel version of the problem, where channels canhave different changepoints. Controlling the False Discovery Rate (FDR), wesimultaneously detect changes in multiple channels. This "local" approach isshown to be more advantageous than multivariate global testing approaches whenthe number of channels with changepoints is much smaller than the total numberof channels.  As a natural application, we consider network-valued time-series and use ourapproach with (a) edges as binary channels and (b) node-degrees or other localsubgraph statistics as count channels. The local testing approach is seen to bemuch more informative than global network changepoint algorithms.

Exact Tests for Offline Changepoint Detection in Multichannel Binary and Count Data with Application to Networks